A rubber cord catapult has a cross-section area of `25mm^(2)` and the initial length of rubber cord is 10 cm . It is stretched by 5 cm and then released to project a missile of mass 5 g. Taking , ` Y_("rubber")= 5xx 10 ^(8) N//m^(2)` , velocity of the projected missile is

Options

A. 20 m/s
B. 100 m/s
C. 250 m/s
D. 200 m/s

Answer

C

Explanation

Potential energy is stored in the rubber cord catapult will be converted into kinetic energy of mass. Thus,
`(1)/(2)mv^(2)=(1)/(2)(YA l^(2))/(L)`
`impliesv=sqrt((YA l^(2))/(mL))`
`v=sqrt((5xx10^(8)xx25xx10^(-6)xx(5xx10^(-2))^(2))/(5xx10^(-3)xx10xx10^(-2)))`
`=250m//s`.